Question

Write the equation of the line in point-slope form and in slope-intercept form.The line passes through the point (6,1) and has a slope of -1/2.

Answer 1

Step-by-step explanation

The slope-intercept form of a line is given as;

`y=mx+b`

The point-slope form of a line is given as;

`y-y_1=m(x-x_1)`

From the given question we have that;

`\begin{gathered} m=-(1)/(2) \\ (x_1,y_1)=(6,1) \end{gathered}`

Part A

Therefore, the point-slope equation can be expressed as;

Answer

`y-1=-(1)/(2)(x-6)`

Part B

To find the slope-intercept form of the line we will simplify the point-slope form. This can be seen below.

`\begin{gathered} y-1=-(1)/(2)(x-6) \\ y=-(1)/(2)x_{}+(6)/(2)+1 \\ y=-(1)/(2)x+3+1 \\ y=-(1)/(2)x+4 \end{gathered}`

Answer:

`y=-(1)/(2)x+4`